A Logical Analysis of the Interaction between ‘Obligation-to-do’ and ‘Knowingly Doing’

  • Jan Broersen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5076)

Abstract

Within a STIT framework, this paper presents a logical study of the interaction between ‘ought-to-do’, and an epistemic notion of ‘knowingly doing’. We start out with some motivating examples concerning the interaction between action, obligation and knowledge. Then we present a complete temporal STIT logic including operators for action, obligation and knowledge. We use the logic to analyze the examples and discuss open problems.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Horty, J.: Personal communication (2007)Google Scholar
  2. 2.
    Broersen, J.M.: A complete STIT logic for knowledge and action, and some of its applications. In: Baldoni, M., Son, T.C., Riemsdijk, M.B.v., Winikoff, M. (eds.) Proceedings Workshop on Declarative Action Languages and Technologies (DALT) 2008. LNCS. Springer, Heidelberg (to appear, 2008)Google Scholar
  3. 3.
    Herzig, A., Troquard, N.: Knowing How to Play: Uniform Choices in Logics of Agency. In: Weiss, G., Stone, P. (eds.) 5th International Joint Conference on Autonomous Agents & Multi Agent Systems (AAMAS 2006), Hakodate, Japan, May 8-12, pp. 209–216. ACM Press, New York (2006)CrossRefGoogle Scholar
  4. 4.
    Broersen, J., Herzig, A., Troquard, N.: A normal simulation of coalition logic and an epistemic extension. In: Proceedings Theoretical Aspects Rationality and Knowledge (TARK XI), BrusselsGoogle Scholar
  5. 5.
    Balbiani, P., Gasquet, O., Herzig, A., Schwarzentruber, F., Troquard, N.: Coalition games over Kripke semantics: expressiveness and complexity. In: Dègremont, C., Keiff, L., Rückert, H. (eds.) Festschrift in Honour of Shahid Rahman. College Publications (to appear, 2008)Google Scholar
  6. 6.
    Bartha, P.: Conditional obligation, deontic paradoxes, and the logic of agency. Annals of Mathematics and Artificial Intelligence 9(1-2), 1–23 (1993)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Anderson, A.: A reduction of deontic logic to alethic modal logic. Mind 67, 100–103 (1958)CrossRefGoogle Scholar
  8. 8.
    Meyer, J.J.: A different approach to deontic logic: Deontic logic viewed as a variant of dynamic logic. Notre Dame Journal of Formal Logic 29, 109–136 (1988)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Broersen, J.: Modal Action Logics for Reasoning about Reactive Systems. PhD thesis, Faculteit der Exacte Wetenschappen, Vrije Universiteit Amsterdam (February 2003)Google Scholar
  10. 10.
    Emerson, E.: Temporal and modal logic. In: Leeuwen, J.v. (ed.) Handbook of Theoretical Computer Science. Formal Models and Semantics, vol. B, pp. 996–1072. Elsevier Science, Amsterdam (1990)Google Scholar
  11. 11.
    Horty, J.: Agency and Deontic Logic. Oxford University Press, Oxford (2001)MATHGoogle Scholar
  12. 12.
    Alur, R., Henzinger, T., Kupferman, O.: Alternating-time temporal logic. In: Proceedings of the 38th IEEE Symposium on Foundations of Computer Science, Florida (October 1997)Google Scholar
  13. 13.
    Alur, R., Henzinger, T., Kupferman, O.: Alternating-time temporal logic. Journal of the ACM 49(5), 672–713 (2002)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Pauly, M.: A modal logic for coalitional power in games. Journal of Logic and Computation 12(1), 149–166 (2002)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Broersen, J., Herzig, A., Troquard, N.: From coalition logic to STIT. In: Proceedings LCMAS 2005. Electronic Notes in Theoretical Computer Science, vol. 157, pp. 23–35. Elsevier, Amsterdam (2005)Google Scholar
  16. 16.
    Broersen, J., Herzig, A., Troquard, N.: Embedding Alternating-time Temporal Logic in strategic STIT logic of agency. Journal of Logic and Computation 16(5), 559–578 (2006)MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Gabbay, D., Kurucz, A., Wolter, F., Zakharyachev, M.: Many-Dimensional Modal Logics: Theory and Applications. Elsevier, Amsterdam (2003)MATHGoogle Scholar
  18. 18.
    Blackburn, P., Rijke, M.d., Venema, Y.: Modal Logic. Cambridge Tracts in Theoretical Computer Science, vol. 53. Cambridge University Press, Cambridge (2001)MATHGoogle Scholar
  19. 19.
    Belnap, N., Perloff, M., Xu, M.: Facing the future: agents and choices in our indeterminist world, Oxford (2001)Google Scholar
  20. 20.
    Hoek, W.v.d., Wooldridge, M.: Cooperation, knowledge, and time: Alternating-time temporal epistemic logic and its applications. Studia Logica 75(1), 125–157 (2003)MATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Jamroga, W., Hoek, W.v.d.: Agents that know how to play, 63(2) (2004)Google Scholar
  22. 22.
    Jamroga, W., Ågotnes, T.: Constructive knowledge: what agents can achieve under incomplete information. Technical Report IfI-05-10, Institute of Computer Science, Clausthal University of Technology, Clausthal-Zellerfeld (2005)Google Scholar
  23. 23.
    Pacuit, E., Parikh, R., Cogan, E.: The logic of knowledge based obligation. Knowledge, Rationality and Action a subjournal of Synthese 149(2), 311–341 (2006)MATHMathSciNetGoogle Scholar
  24. 24.
    Wansing, H.: Obligations, authorities, and history dependence. In: Wansing, H. (ed.) Essays on Non-classical Logic, pp. 247–258. World Scientific, Singapore (2001)Google Scholar
  25. 25.
    Parikh, R., Ramanujam, R.: A knowledge based semantics of messages. Journal of Logic, Language and Information 12(4), 453–467 (2003)MATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Åqvist, L.: Good samaritans contarary-to-duty imperatives and epistemic obligations. NOUS 1, 361–379 (1967)Google Scholar
  27. 27.
    Wright, G.v.: Deontic logic. Mind 60, 1–15 (1951)CrossRefGoogle Scholar
  28. 28.
    Kooi, B.P., Tamminga, A.M.: Conflicting obligations in multi-agent deontic logic. In: Goble, L., Meyer, J.-J.C. (eds.) DEON 2006. LNCS (LNAI), vol. 4048, pp. 175–186. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  29. 29.
    Broersen, J., Herzig, A., Troquard, N.: A STIT-extension of ATL. In: Fisher, M., van der Hoek, W., Konev, B., Lisitsa, A. (eds.) JELIA 2006. LNCS (LNAI), vol. 4160, pp. 69–81. Springer, Heidelberg (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Jan Broersen
    • 1
  1. 1.Department of Information and Computing SciencesUtrecht UniversityThe Netherlands

Personalised recommendations